2.63 hours
<h2>Explanation:</h2>First we have to read carefully the problem, It start telling us that <u>Emily </u>was driving with average velocity of <em>87.5 km/h to the north</em>. Velocity is a physical variable that is definded in terms of :
- Speed of the object (<em>87.5 km/h</em>)
- Direction of the object (<em>north</em>)
Them the problem says that <u>Emily's trip has an average velocity of </u><u><em>76.8 km/h to the north </em></u>because she made a rest stop for 22 minutes<u><em>.</em></u>
Now you can ask yourself: If Emily was driving at <em>87.5 km/h, why the average speed of the trip was </em><u><em>76.8 km/h?</em></u>
we need to see how speed is defined:
<em>***Note 1: </em>
- Distance will be called as<em> "x" </em>and units will be kilometers(<em>km</em>)
- Time will be called as <em>"y" </em>and units will be hours(<em>h</em>)
So, 87.5 km/h would be the average speed for a distance "x" and a time "y" without stops. But Emily made a stop that took 22 minutes. For the same distance Emily's trip took more time and time is in the denominator. If our numerator is constant and our denominator gets higher, the final result will be lower
Now, we have the follow expressions:
***Note 2:
- we need to convert 22 <em>minutes</em> to <em>hours</em>. 1 <em>hour</em>= 60 <em>minutes</em>, so we need to apply the follow covert factor:
The problem aks us about how long does the trip take, it means that we have to find y.
We have two variables (x and y), and we have two equationts. We know that x have the same value for both problems (Because both average speeds have the same distance), so we can solve both equations for x and made equal each other
We have to expand (5) and then we have to solve for y